#  Replication Data for: Machine Learning for Improved Current Density Reconstruction from 2D Vector Magnetic Images


## Overview

This repository contains the dataset and associated resources used in the scientific paper titled **"Machine Learning for Improved Current Density Reconstruction from 2D Vector Magnetic Images"**. The dataset includes:

- **Trained Neural Network Models**: Pre-trained models ready for inference.
- **Validation Data**: Dataset used for validating model performance plus experimental data, including all configurations shown in paper.
- **Training Code**: Scripts for training neural networks.
- **Inference Scripts**: Tools for performing inference using the pre-trained models.
- **Data Analysis Scripts**: Scripts for analyzing the results and visualizing performance metrics.
- **Data Generations Scripts**: Scripts for generating new training and validation data
- **Fourier Inversion code**: Code used for Fourier Method comparisons in the paper

## Contents

1. [Citation](#citation)
2. [Getting Started](#getting-started)
3. [Performing Inference](#performing-inference)
4. [Training New Models](#training-new-models)
5. [Training Datasets](#training-datasets)
6. [Data Description](#data-description)
7. [Data Generation](#data-generation)
8. [Fourier Inversion](#fourier-inversion)
9. [Data Analysis](#data-analysis)
10. [Acknowledgements](#acknowledgements)
11. [License](#license)

---

## Citation

If you use this dataset or associated scripts in your research, please cite the following paper and/or dataset:

```
@article{reed_machine_2024,
	title = {Machine {Learning} for {Improved} {Current} {Density} {Reconstruction} from {2D} {Vector} {Magnetic} {Images}},
	url = {http://arxiv.org/abs/2407.14553},
	publisher = {arXiv},
	author = {Reed, Niko R. and Bhutto, Danyal and Turner, Matthew J. and Daly, Declan M. and Oliver, Sean M. and Tang, Jiashen and Olsson, Kevin S. and Langellier, Nicholas and Ku, Mark J. H. and Rosen, Matthew S. and Walsworth, Ronald L.},
	month = jul,
	year = {2024},
}

@data{DVN/SD6PVP_2025,
author = {Reed, Niko and Bhutto, Danyal and Turner, Matthew and Daly, Declan and Oliver, Sean and Tang, Jiashen and Olsson, Kevin and Ku, Mark and Rosen, Matthew and Walsworth, Ronald},
publisher = {Harvard Dataverse},
title = {{Replication Data for: Machine Learning for Improved Current Density Reconstruction from 2D Vector Magnetic Images}},
year = {2025},
version = {DRAFT VERSION},
doi = {10.7910/DVN/SD6PVP},
url = {https://doi.org/10.7910/DVN/SD6PVP}
}

```

---


## Getting Started

### Prerequisites

Ensure you have the following installed:

- Python 3.8 or higher
- Required Python libraries (listed in `requirements.txt`)
    - Note tensorflow must be 2.15.0 or **less** for the provided inference code to load the saved models

### Installation

1. Download this repository
2. Download one of the provided training sets 


3. Install dependencies:
   ```bash
   pip install -r requirements.txt
   ```

---

## Performing Inference

1. Import libraries (tensorflow version <= 2.15)
```python
   import tensorflow as tf
   import numpy as np
   ```
2. Load validation data
3. Define a function that accounts for the re-scaling the network experienced during training:
  ```python
def UNET_normalized_inference(data_in_temp, model):
    
    # Calculate vector norms
    vect_norm = (data_in_temp[:, :, :, 0]**2 +
                 data_in_temp[:, :, :, 1]**2 +
                 data_in_temp[:, :, :, 2]**2)**0.5
    vect_norm = np.max(vect_norm, axis=1)
    vect_norm = np.max(vect_norm, axis=1)

    file_size = np.size(vect_norm)
    for j in range(file_size):
        if vect_norm[j] != 0:
            data_in_temp[j, :, :, :] = data_in_temp[j, :, :, :] / vect_norm[j]

    # Make predictions
    pred_jx, pred_jy = model.predict(data_in_temp)
    data_out_temp = np.zeros([file_size, 64, 64, 2])

    for j in range(file_size):
        if vect_norm[j] != 0:
            data_out_temp[j, :, :, 0] = pred_jx[j, :, :, 0] * vect_norm[j] * 1e11
            data_out_temp[j, :, :, 1] = pred_jy[j, :, :, 0] * vect_norm[j] * 1e11

    return data_out_temp
```

4. Load model and perform inference
```python
model = tf.keras.models.load_model(model_dir)
current_density_predictions = UNET_normalized_inference(magnetic_field_data,model)
```


---

## Training New Models

1. Prepare your training data (we recommend re-scaling both B and J)
2. Update the config file (`configs/train.json`) to indicate the directory of your training & test data, and customize other parameters
3. Run the training script:
   ```bash
   python unet_main_train.py -c configs/train.json
   ```
3. Monitor training progress:
   - Train and test loss are printed and saved to train_loss and val_loss files
   - The model is saved in the a directory named `checkpoints/` within the folder created in the `experiments` directory based on the run name in the config file

### Configuration

Variable defintions for config file

Here is the list of variables from the JSON file, formatted in markdown with inline backticks (`):  

- `exp_name` name of the directory that will be created for the trained model
- `resume` if set to 0 the code will create a new model. If set to 1 it will attempt to load a model from `loadmodel_dir` and continue training. 
- `num_epochs` number of times the model will see each file in the training set
- `num_files` number of files in the training set (code assumes training files end in XXX format from 001 to `num_files`)
- `batch_size` number of configurations processed at once during training. 
- `im_h` vertical resolution of training data
- `im_w` horizontal resolution of training data
- `noise` Set to `True` if noise sholuld be added during training, and `False` otherwise
- `mean_noise` Standard deviation of additive Gaussian noise drawn from N(0,`mean_noise`)
- `data_dir` Directory of training data
- `train_input` File string of input (Bxyz) training data (not including numbers or `.npy`)
- `train_output` File string of ground truth/output (Jxy) training data (not including numbers or `.npy`)
- `test_input` Complete file path of validation input (We usually reserve 000 file for this)
- `test_output` Complete file path of validation output 
- `learning_rate` Sets learning rate for model. 1e-4 or 1e-5 generallyl works well
  

---

## Training Datasets

The following datasets are available for training:

- **50 micron and 64x64 resolution**: [https://doi.org/10.7910/DVN/QPCS0I](https://doi.org/10.7910/DVN/QPCS0I)
- **50 micron and 256x256 resolution**: [https://doi.org/10.7910/DVN/OPEX5N](https://doi.org/10.7910/DVN/OPEX5N)
- **500 micron and 64x64 resolution**: [https://doi.org/10.7910/DVN/SJDS2O](https://doi.org/10.7910/DVN/SJDS2O)

Note that while these datasets were generated from the same data distribution as the data used to train the models, none of the included configurations were used in our training set. Thefore, all data in these collections can also serve as validation data to our trained networks.

---

## Data Description

All data has the following structure:

`[configuration index, spatial x, spatial y, component]`

Components are ordered, x, y, z.

We provide the following categories of data:

1. **Simulated In-Distribution Validation Data**: Validation data generated under conditions similar to the training data distribution; files include the configurations feautred in the paper figures. Note some validation files have data sorted by type (i.e first half of indices are type 1, second half are type 2)

2. **Simulated Out-of-Distribution Validation Data**: Validation data designed to test the model's performance under conditions outside the training data distribution.

3. **Experimental Data**: Data measured from a known current density distribution using nitrogen vacancy center magnetometry. For more details about the experimental setup, please refer to the supplemental information in the associated paper. Experimental data was taken at a variety of standoff distances, which can be estimated from the properties of the measured magnetic field.

   - Experimental data is available in the following resolutions:
     - **64x64 resolution**
     - **230x230 resolution**

### Parameters used to generate training and validation data:

| Parameter                    | Class I                                              | Class II                                             |
|------------------------------|-----------------------------------------------------|-----------------------------------------------------|
| Class of wire               | Curves formed by interpolating 2-21 randomly         | Thin right angle segments, thin arbitrary angle     |
|                              | generated points (with cropping)                    | segments, thick straight wires                     |
| Number of independent wires  | 1                                                   | 1, 2, or 3                                          |
| Field of view                | 2 mm                                                | 2 mm                                                |
| Standoff distance            | 50 ± 10 µm (500 ± 50 µm for large standoff)         | 50 ± 10 µm (500 ± 50 µm for large standoff)        |
| Thickness of current layer   | 14 µm                                               | 14 µm                                               |
| Width of wires (% of dataset)| 16-160 µm (50%), 160-320 µm (50%)                   | 9-30 µm (67%), 97-156 µm (33%)                     |
| Approximate Current Range    | 15.5 - 311 mA                                       | 1.95 - 170 mA                                       |



---

## Data Generation

Instructions for using our data generation code. Note that while a 75,000 configurations of type 2 data can be generated in a few hours, generating the same quantity of type 1 data takes many days due to the more intensive current density simulation process.

### Requirements

COMSOL LiveLink (see https://doc.comsol.com/5.4/doc/com.comsol.help.llmatlab/LiveLinkForMATLABUsersGuide.pdf), Matlab, Python.

### Type 1 Data

#### Main files:
- `COMSOLstudy_trial2.m`
    - change `runNum` and `Iterations` variables. See comment in the program
    - change `filepathmain` and `imgpathmain`. See comment in the program
#### Dependent files:
- `fgenerateRandomGNDTERMLabel.m`
- `fgenerateRandomCurrent.m`
- `fgenerateRandomSplineCoord.m`
- `fgenerateRandomWidth.m`
- `fsetupCOMSOL.m`

#### Other files
- `compressImages.m`:
	   - remove the first two columns of current data, which is X Y position information, only leave the Jx and Jy
	- also remove the cases where current path doesn't cross region of interest
	- generates a MATLAB variable called `problematicls`
- `deleteFiles.m`
	- use `problematicls` to remove those empty data in mesh images and uncompressed current data files
- `renameFiles.m`
	- shuffle data namings after using deleteFiles.m, make sure file namings run from 1 to N uninterrupted. 

#### Generation Instructions

1. Simulate current densities using COMSOL & matlab by running `\data_generation\type1\generate_current_densities.m` through COMSOL LiveLink for Matlab 
2. Process current densities into magnetic fields using `\data_generation\type1\process_current_densities.m` (MATLAB)
3. Convert `.mat` files to `.npy` using `\data_generation\file_converter.py` (Python)
4. If you didn't use `deleteFiles.m`, identify and replace probelmatic configurations using `\data_generation\fix_problems.py` (Python)

### Type 2 Data

#### Main files:
- Variables in `generate_and_process.m` 
    - `save_dirc` directory where files will be saved
    - `M` number of images/file
    - `num_batches` number of files
    - `device_x_dimension` length of field of view (m)
    - `res=1024` resolution during FFT processing
    - `padding` padding to prevent FFT artifacts
    - `standoff` mean standoff distance
    - `stadoff_std` standard deviation of standoff distance
    - `depth of current source` thickness of wire in out of plane direction
    - `tot_current` average current flowing through wire (A)
    - `sigma` resolution, determined by the larger of optical diffraction or pixel size

#### Dependent files:
- `BinImage.m`
- `RightAngle2.m`
- `Slope2.m`
- `WideSlope2.m`

Parameters of wire thickness, shape, etc. can be modified using these functions.

1. Simulate current densities using `\data_generation\type2\generate_and_process.m` (MATLAB). Make sure associated functions are in same directory as file path
2. Convert `.mat` files to `.npy` using `\data_generation\file_converter.py` (Python)

### Creating Training and Validation Data

1. (If desired) Run script to combine type 1 and type 2 data `\data_generation\blend_2types.py` (Python)
2. Normalize/scale data for optimal training. Image normalization can be turned on for Bxyz by changing the `image_normalization` variable in the above script. We recommend scaling Jxy by a factor of 1e8


---

## Fourier Inversion

Code used for Fourier inversion that formed the basis of comparison for our paper can be found in the `ComparisonAndAnalysis.ipynb` notebook.

There are two optimizable parameters for the Fourier Method at each standoff. These were determined by performing a bivariable optimization proceedure to determine the pair of values that maxmized Fourier Method SSIM for a noise level of 0.2

---
## Data Analysis

Code used to calculate SSIM, RMSE, and PSNR as a function of noise can be found in the `ComparisonAndAnalysis.ipynb` notebook under `Quantitative Analysis` section. This data can be saved as a dictionary and/or a plain text file.

---

## Acknowledgements

This work builds upon methodologies described in the following paper:

B. Zhu, J. Z. Liu, S. F. Cauley, B. R. Rosen, and M. S. Rosen, “Image reconstruction by domain-transform manifold learning,” Nature, vol. 555, no. 7697, pp. 487 EP ––492, Mar. 2018

---

## License

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8. Termination.
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However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation.

Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice.

Termination of your rights under this section does not terminate the licenses of parties who have received copies or rights from you under this License. If your rights have been terminated and not permanently reinstated, you do not qualify to receive new licenses for the same material under section 10.

9. Acceptance Not Required for Having Copies.
You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.

10. Automatic Licensing of Downstream Recipients.
Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License.

An “entity transaction” is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party's predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts.

You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.

11. Patents.
A “contributor” is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor's “contributor version”.

A contributor's “essential patent claims” are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, “control” includes the right to grant patent sublicenses in a manner consistent with the requirements of this License.

Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contributor's essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version.

In the following three paragraphs, a “patent license” is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To “grant” such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party.

If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. “Knowingly relying” means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient's use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid.

If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it.

A patent license is “discriminatory” if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007.

Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.

12. No Surrender of Others' Freedom.
If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.

13. Use with the GNU Affero General Public License.
Notwithstanding any other provision of this License, you have permission to link or combine any covered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.

14. Revised Versions of this License.
The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns.

Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License “or any later version” applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation.

If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy's public statement of acceptance of a version permanently authorizes you to choose that version for the Program.

Later license versions may give you additional or different permissions. However, no additional obligations are imposed on any author or copyright holder as a result of your choosing to follow a later version.

15. Disclaimer of Warranty.
THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM “AS IS” WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.

16. Limitation of Liability.
IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.

17. Interpretation of Sections 15 and 16.
If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee.

END OF TERMS AND CONDITIONS


